[milesrout]

No, functions aren't first class in C. When you use a function in an expression it undergoes lvalue conversion and "decays" to a pointer to the function. You can only call, store, etc function pointers, not functions. Function pointers are first class. Functions are not as you can't create them at runtime.

A functional programming language is one with first class functions.

[grandempire]

What is the impact on the user of having first class functions vs first class function pointers?

Last I checked when you implement lambda in lisp it's also a pointer to the lambda internally.

[xigoi]

Function pointers can’t close over variables.

[vkazanov]

The other important bit here is garbage collection.

Local and anonymous functions that capture lexical environments really, really work much better in languages built around GCs.

Without garbage collection a trivial closure (as in javascript or lisps) suddenly needs to make a lot of decisions around referencing data that can be either on the stack or in the heap.

[grandempire]

C++ does this and the decision to make is to capture by reference or value.

Environments aren’t a thing in Haskell etc. does that mean it’s not functional?

[vkazanov]

Yes, C++ is a great example of having to make decisions that don't have good solutions without a GC or something like. See mentions of undefined behaviour in relevant sections of the standard, i.e. when a lambda captures something with a limited lifetime.

Are you saying that Haskell doesn't have lexical environments? It very much does, just as all major languages of the ML language family do.

[grandempire]

That has nothing to do with the value/pointer distinction.

And “close over” semantics differ greatly depending on the language.